Left-back Tagliafico signed a four-and-a-half-year contract in Amsterdam on Friday and joins for an undisclosed fee.
The 25-year-old made his Argentina debut last June as Jorge Sampaoli guided the Albiceleste to a 1-0 victory over Brazil in his first match at the helm.
Tagliafico, whose only previous spell in Europe was a season on loan at Real Murcia in the Spanish second tier, was a key member of the Independiente side that won the Copa Sudamericana in December.
His arrival came on a busy day for Ajax, who also announced a two-year contract extension for Donny van de Beek, who is now tied to the club until June 2022.
Furthermore, the Eredivisie side confirmed the impending arrival of Hoffenheim assistant Alfred Schreuder as part of new coach Erik ten Hag's backroom staff.